Problem: Find a nonzero $p$ such that $px^2-12x+4=0$ has only one solution.
Solution: For a quadratic to have only one solution, the discriminant must be zero. Therefore, we have $(-12)^2-4 \cdot p \cdot 4 = 0$. Solving, we get $(-12)^2-4 \cdot p \cdot 4 = 144-16p = 0$. Thus, $144=16p$, so $p=\boxed{9}$.